Numerical method for stability analysis of functionally graded beams on elastic foundation

• Numerical method for stability analysis of axially functionally graded (FG) Euler–Bernoulli beams.
• The method of initial parameter in differential form is used.
• Richardson extrapolation method is employed to improve the accuracy of results.

This paper considers the problems of stability of non-uniform and axially functionally graded (FG) Euler–Bernoulli beams on elastic foundation. The boundary conditions of the beam are given in general form covering different classical supporting conditions. Furthermore, the boundary conditions are transformed into convenient form in order to avoid handling infinity values of the stiffness coefficients. The method of initial parameters in differential form is used for the numerical solution of the problem. The solution of the posed boundary value problem is reduced to the iterative solution of two initial value problems and homogeneous linear algebraic system of order two. The Richardson extrapolation method is employed to improve the accuracy of results. The performance of the method proposed has been validated by several numerical examples.